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This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers.

Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet-Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement-Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups.

The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.

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- Notes on the Geometric Satake Equivalence. - Distinguished Representations of Reductive p -Adic Groups. - Period Integrals of Automorphic Forms and Local Distinction. - The Trace Formula and the Proof of the Global Jacquet-Langlands Correspondence. - Distinction of Representations via Bruhat-Tits Buildings of p -Adic Groups. - Towards Generalized Prehomogeneous Zeta Integrals. - Functoriality and the Trace Formula. - Sur les paquets d´Arthur des groupes classiques et unitaires non quasi-déployés.

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Volker Heiermann is a Professor of Mathematics at the Aix Marseille Université, Luminy.
Dipendra Prasad is a Professor of Mathematics at the Tata Institute of Fundamental Research, Mumbai.
The authors are established researchers in the broad subject of Automorphic forms who came together at CIRM Luminy during the first half of 2016 on Chaire Morlet,a distinguished research Chaire created by the CIRM, Aix Marseille University, the city of Marseille.

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